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Titlebook: Submanifold Theory; Beyond an Introducti Marcos Dajczer,Ruy Tojeiro Textbook 2019 Springer Science+Business Media, LLC, part of Springer Na

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书目名称Submanifold Theory
副标题Beyond an Introducti
编辑Marcos Dajczer,Ruy Tojeiro
视频video
概述Provides a comprehensive introduction to submanifold theory.Engages the reader throughout with many examples and exercises.Reaches the frontier of knowledge in the subject?
丛书名称Universitext
图书封面Titlebook: Submanifold Theory; Beyond an Introducti Marcos Dajczer,Ruy Tojeiro Textbook 2019 Springer Science+Business Media, LLC, part of Springer Na
描述.This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme is the isometric and conformal deformation problem for submanifolds of arbitrary dimension and codimension. Several relevant classes of submanifolds are also discussed, including constant curvature submanifolds, submanifolds of nonpositive extrinsic curvature, conformally flat submanifolds and real Kaehler submanifolds. This is the first textbook to treat a substantial proportion of the material presented here. The first chapters are suitable for an introductory course on Submanifold theory for students with a basic background on Riemannian geometry. The remaining chapters could be used in a more advanced course by students aiming at initiating research on the subject, and are also intended to serve as a reference for specialists in the field..
出版日期Textbook 2019
关键词conformal immersion; isometric immersion; rigidity and deformation; submanifold; Submanifold theory; conf
版次1
doihttps://doi.org/10.1007/978-1-4939-9644-5
isbn_ebook978-1-4939-9644-5Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Science+Business Media, LLC, part of Springer Nature 2019
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Submanifolds with Relative Nullity,Several of the results of Chaps. . and . have provided relevant geometric conditions under which a submanifold of a space form must have positive index of relative nullity at any point. The aim of this chapter is to study submanifolds that have this property.
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Isometric Immersions of Warped Products,In this chapter we discuss two other useful ways of constructing immersions of product manifolds from immersions of the factors, with an increasing degree of generality. Namely, we introduce the notions of (extrinsic) warped products of immersions and, more generally, of partial tubes over extrinsic products of immersions.
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Conformally Flat Submanifolds,This chapter brings us back to the conformal realm. Here our main interest is on geometric and topological properties of conformally flat submanifolds of Euclidean space, that is, isometric immersions into Euclidean space of Riemannian manifolds that are locally conformally diffeomorphic to an open subset of Euclidean space.
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Submanifold Theory978-1-4939-9644-5Series ISSN 0172-5939 Series E-ISSN 2191-6675
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